School Segregation Index Descriptive Report
Minnesota School District-Level Indices
How do segregation trends across the Twin Cities 7-county metro compare to each other?
Exposure/Interaction Index
The Exposure/Interaction Index is a measure of segregation. It estimates the probability of members of specific groups interacting with members of another specific group. In the case of school segregation, it measures the probability that students of racial group A will interact with students of racial group B in a specific school within the district. This measure takes into account the proportion of students of each race within a district that attend each school. See the Census Bureau’s brief for more information on this index.
\[Interaction = \sum_{i=1}^n \left( \frac{B_i}{B} \right) \left( \frac{W_i}{T_i} \right)\]
Where:
- \(B_i\) is the number of students of a particular racial group in a school \(i\).
- \(B\) is the total number of students of the same racial group in the entire district.
- \(W_i\) is the number of White students in school \(i\).
- \(T_i\) is the total student enrollment of the school district \(i\).
- \(n\) is the number of schools in the district.
Exposure Index Limitations
Isolation Index
Isolation index is a measure of…
\[Isolation = \sum_{i=1}^{n} \left(\frac{B_i}{B} \right) \left(\frac{B{_i}}{T_i} \right)\] Where:
- \(B_i\) is the number of students of a particular racial group in a school \(i\).
- \(B\) is the total number of students of the same racial group in the entire district.
- \(T_i\) is the total student enrollment of the district \(i\).
- \(n\) is the number of schools in the district.
Isolation Index Metrics
I have not yet understood which are the Isolation Index measures we should use from Stanford’s Administrative dataset. There are many to choose from. We also have to identify what geographies we want to measure across.
Normalized Exposure Index
According to Education Opportunity’s website, the normalized exposure index measures: “the difference between two groups’ exposure to one of the groups. For example, the White-Hispanic normalized exposure index compares the proportions of White (or Hispanic, equivalently) students in the average White and Hispanic students’ schools. A White-Hispanic normalized exposure value of 0.5 indicates that the proportion of White students in the average White student’s school is 50 percentage points higher than in the average Hispanic student’s school (ignoring the presence of other groups aside from the racial dyad of interest).”
Dissimilarity Index
The Dissimilarity index is another measure of segregation. According to the census bureau, the dissimilarity measures the proportion of one group that would have to move to another area to be distributed equally as a comparison group. It can be interpreted in the following way: “A dissimilarity index of 0 indicates conditions of total integration under which both groups are distributed in the same proportions across all neighborhoods. A dissimilarity index of 100 indicates conditions of total segregation such that the members of one group are located in completely different neighborhoods than the second group.”
Dissimilarity index is calculated following Wang et al.’s, methods found here.
\[Dissimilarity = \frac{1}{2} \sum_{i=1}^{n} \left|\frac{b_i}{B} - \frac{w{_i}}{W} \right|\] Where:
- \(b_i\) is the number of students of a particular racial group in school \(i\).
- \(B\) is the total number of students of the same racial group enrolled in the district.
- \(w_i\) is the number of white students in school \(i\).
- \(W\) is the total number of white students enrolled in the district.
- \(n\) is the number of schools in the district.
Information Theory Index Plot
Difference in Exposure to Free Lunch
CBSA-Level Segregation Indices
How do segregation trends in the Twin Cities compare to other cities in the US?
The following analysis compares Twin Cities between-school segregation trends to other US major cities. The first charts highlight city-level trends and the following compares those trends across cities. Only the top 20 CBSA’s by student population were used for these plots. Given the length of the CBSA names, they have been shortened to be legible in these crowded plots. Reference the following table for the abbreviated names:
cbsa %>%
filter(year==2022) %>%
group_by(cbsa23name) %>%
summarise(tot = sum(tot)) %>%
arrange(desc(tot)) %>%
top_n(n = 20) %>%
select(long = "cbsa23name") %>%
mutate(
short = str_extract_all(long, "^[^-]+|(?<=, )[^-]+") %>%
sapply(paste, collapse = ", ")
) %>%
gt() %>%
tab_header(
title = "Twin Cities Metro School Closures, 2001-2022",
subtitle = ""
) %>%
opt_align_table_header(align = "center") %>%
cols_align(
align = c("center"),
columns = everything()
) %>%
tab_source_note(
source_note = "Data source is the Stanford Segregation Dataset from Education Opportunity."
) %>%
cols_label(
long = "Full CBSA Name",
short = "Short CBSA Name",
) %>%
tab_style(locations = cells_body(),
style = cell_text(transform = "uppercase", v_align = "bottom", weight = 400)) %>%
tab_style(locations = cells_title("title"),
style = cell_text(transform = "uppercase", v_align = "bottom", weight = 700)) %>%
tab_style(locations = cells_title("subtitle"),
style = cell_text(transform = "uppercase", v_align = "bottom", weight = 500)) %>%
tab_style(style = list(cell_borders(sides = "top", color = "black", weight = px(0)), cell_text(transform = "uppercase", v_align = "bottom", size = px(14), weight = 500)),
locations = gt::cells_column_labels(columns = gt::everything())) %>%
tab_style(style = cell_borders(sides = "bottom",
color = "black",
weight = px(1)),
locations = cells_row_groups()) %>%
tab_options(column_labels.background.color = "white",
data_row.padding = px(3),
heading.border.bottom.style = "none",
table.border.top.width = px(3),
table.border.top.style = "none",
table.border.bottom.style = "none",
column_labels.font.weight = "normal",
column_labels.border.top.style = "none",
column_labels.border.bottom.width = px(2),
column_labels.border.bottom.color = "black",
row_group.border.top.style = "none",
row_group.border.top.color = "black",
row_group.border.bottom.width = px(1),
row_group.border.bottom.color = "white",
stub.border.color = "white",
stub.border.width = px(0),
source_notes.font.size = 12,
source_notes.border.lr.style = "none",
table.font.size = 12)| Twin Cities Metro School Closures, 2001-2022 | |
| Full CBSA Name | Short CBSA Name |
|---|---|
| New York-Newark-Jersey City, NY-NJ | New York, NY |
| Los Angeles-Long Beach-Anaheim, CA | Los Angeles, CA |
| Dallas-Fort Worth-Arlington, TX | Dallas, TX |
| Houston-Pasadena-The Woodlands, TX | Houston, TX |
| Chicago-Naperville-Elgin, IL-IN | Chicago, IL |
| Atlanta-Sandy Springs-Roswell, GA | Atlanta, GA |
| Washington-Arlington-Alexandria, DC-VA-MD-WV | Washington, DC |
| Philadelphia-Camden-Wilmington, PA-NJ-DE-MD | Philadelphia, PA |
| Riverside-San Bernardino-Ontario, CA | Riverside, CA |
| Miami-Fort Lauderdale-West Palm Beach, FL | Miami, FL |
| Phoenix-Mesa-Chandler, AZ | Phoenix, AZ |
| Boston-Cambridge-Newton, MA-NH | Boston, MA |
| Detroit-Warren-Dearborn, MI | Detroit, MI |
| Minneapolis-St. Paul-Bloomington, MN-WI | Minneapolis, MN |
| San Francisco-Oakland-Fremont, CA | San Francisco, CA |
| Seattle-Tacoma-Bellevue, WA | Seattle, WA |
| San Antonio-New Braunfels, TX | San Antonio, TX |
| San Diego-Chula Vista-Carlsbad, CA | San Diego, CA |
| Charlotte-Concord-Gastonia, NC-SC | Charlotte, NC |
| Denver-Aurora-Centennial, CO | Denver, CO |
| Data source is the Stanford Segregation Dataset from Education Opportunity. | |
Exposure Index
Isolation Index
Normalized Exposure Index
Dissimilarity Index
Information Theory Index
Difference in Exposure to Free Lunch
